Chapter 5 Polynomials and Polynomial Functions

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• Lesson 4-2 Graphing Quadratic Functions

  Graph each function.

  1. f ( x ) = x 2 − 8 x + 7 f open x close equals , x squared , minus 8 x plus 7
  2. f ( x ) = − 1 2 x 2 − 4 x − 4 f open x close equals negative , 1 half , x squared , minus 4 x minus 4
  3. f ( x ) = x 2 + 4 x + 4 f open x close equals , x squared , plus 4 x plus 4

• Lesson 4-3 Writing Equations of Parabolas

  Write in standard form the equation of the parabola passing through the given points.

  4. ( − 1 , − 6 ) , ( − 3 , − 4 ) , ( 2 , 6 ) open negative 1 comma negative 6 close comma open negative 3 comma negative 4 close comma open 2 comma 6 close
  5. ( 3 , 4 ) , ( − 2 , 9 ) , ( 2 , 1 ) open 3 comma 4 close comma open negative 2 comma 9 close comma open 2 comma 1 close
  6. ( − 5 , − 8 ) , ( 4 , − 8 ) , ( − 3 , 6 ) open negative 5 comma negative 8 close comma open 4 comma negative 8 close comma open negative 3 comma 6 close

• Lesson 4-5 Solving Quadratic Equations by Graphing

  Solve each equation by graphing. Round to the nearest hundredth.

  7. 1 = 4 x 2 + 3 x 1 equals , 4 x squared , plus 3 x
  8. 1 2 x 2 + x − 14 = 0 1 half , x squared , plus x minus 14 equals 0
  9. 5 x 2 + 30 x = 12 5 x squared , plus 30 x equals 12

• Lesson 4-5 Solving Quadratic Equations by Factoring

  Solve each equation by factoring.

  10. x 2 − x − 20 = 0 x squared , minus x minus 20 equals 0
  11. x 2 + 6 x − 27 = 0 x squared , plus 6 x minus 27 equals 0
  12. 3 x 2 − 9 x + 6 = 0 3 x squared , minus 9 x plus 6 equals 0

• Lesson 4-7 Finding the Number and Type of Solutions

  Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary.

  13. x 2 − 12 x + 30 = 0 x squared , minus 12 x plus 30 equals 0
  14. − 4 x 2 + 20 x − 25 = 0 negative 4 , x squared , plus 20 x minus 25 equals 0
  15. 2 x 2 = 8 x − 8 2 x squared , equals 8 x minus 8

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